Certainly the choosing by lots methodology seems to have died out during the early Christian era. The (Jewish) Apostles choosing Matthias may have continued using their Jewish methodology for a while; I’m not aware of any record of either for or against.
The Apostles most certainly exercised their authority in choosing a replacement Apostle. The only thing that we may look at slightly askance at is in their methodology. Not in the fact that they did decide to replace Judas.
The selection of Paul would seem to be outside of the normal selection methodology; but that is for God to decide and to do, not man. All we can do is utilize the methodology that we were shown.
Just because they decided to replace Judas does not mean ipso facto that they had the authority to do so. What is an Apostle? The word means "one who is sent". Sent by whom? By God, of course. So it was God who had the only authority, not the Apostles. They "could" have made a mistake, that is unclear. The 11 chose to roll the dice. God either blessed (caused) the result or He did not. But whether the 12th Apostle was Matthias or Paul (or anyone else) was SOLELY within God's authority, not man's.